Pointwise blow-up phenomena for a Dirichlet problem
| Autor: | Maristella Petralla, Pierpaolo Esposito |
|---|---|
| Přispěvatelé: | Esposito, Pierpaolo, Petralla, M. |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Pointwise
Dirichlet problem Pure mathematics Applied Mathematics Mathematical analysis Morse code law.invention Blow-up Classification results Morse index Non-degeneracy Rozenblyum-Lieb-Cwikel inequality law Bounded function Uniform boundedness sort A priori and a posteriori Equivalence (formal languages) Analysis Mathematics |
| Popis: | For the Dirichlet problem $$-\Delta u+\lambda V(x) u=u^p in \Omega\\ u=0 on \partial \Omega,$$ with $\Omega \subset R^N$, $N\geq 2$, a bounded domain and $p>1$, blow-up phenomena necessarily arise as $\lambda \to +\infty$. In the present paper, we address the asymptotic description for pointwise blow-up, as it occurs when either the ``energy" or the Morse index is uniformly bounded. A posteriori, we obtain an equivalence between the two quantities in the form of a double-side bound with essentially optimal constants, a sort of improved Rozenblyum-Lieb-Cwikel inequality for the equation under exam. Moreover, we prove the nondegeneracy of any ``low energy" or Morse index $1$ solution under a suitable condition on the potential. |
| Databáze: | OpenAIRE |
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